Answer:
B) The margin of error is 0.0269.
C) The confidence interval is (0.5406, 0.5944).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In the poll, n=918 and x=521 who said "yes."
This means that [tex]n = 918, \pi = \frac{521}{918} = 0.5675[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
B) Identify the value of the margin of error E.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.5675*0.4325}{918}} = 0.0269[/tex]
The margin of error is 0.0269.
C) construct the confidence interval.
[tex]\pi \pm M[/tex]
So
[tex]\pi - M = 0.5675 - 0.0269 = 0.5406[/tex]
[tex]\pi + M = 0.5675 + 0.0269 = 0.5944[/tex]
The confidence interval is (0.5406, 0.5944).
A restaurant can seat 100 diners. Four of
the tables can each seat 6 people. The
rest of the tables can each seat 4 people.
How many tables does the restaurant
have in all?
100 people
6x4= 24
100-24= 76
76÷4= 19
19+4=23
lmk if I'm wrong
PLZ HELP IM BEGGING
Find the volume of this prism
Answer:
345.6
Step-by-step explanation:
Admission prices at a football game were $5 for adults and $ 2 for children.
The total value of the tickets sold was $2520, and 654 tickets were sold. How many adult
tickets and how many child tickets were sold?
Show all six steps.
Answer:
404 adult tickets were sold, and 250 child tickets.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that
x is the number of adult tickets sold.
y is the number of child tickets sold.
654 tickets were sold.
This means that
[tex]x + y = 654[/tex]
[tex]y = 654 - x[/tex]
Admission prices at a football game were $5 for adults and $ 2 for children. The total value of the tickets sold was $2520.
This means that
[tex]5x + 2y = 2520[/tex]
Since [tex]y = 654 - x[/tex]
[tex]5x + 2(654 - x) = 2520[/tex]
[tex]5x + 1308 - 2x = 2520[/tex]
[tex]3x = 1212[/tex]
[tex]x = \frac{1212}{3}[/tex]
[tex]x = 404[/tex]
[tex]y = 654 - x = 654 - 404 = 250[/tex]
404 adult tickets were sold, and 250 child tickets.
Just c please
Thanks will give brainliest
pyramid A: 16 + [tex]8\sqrt{5[/tex]
pyramid B: 400 + [tex]8\sqrt{125[/tex]
pyramid A: 4 by 4= 16 cm.
with a height of 1 and length of 2, we use pythagorean theorem to find height of other surfaces to be square root of 5. area of triangle is 1/2 bh
square root of 5 multiplied by 4 and divided by 2 is 2 root 5
multiply this by 4 sides total for 8 root 5
Add the 8 root 5 to 16
To find pyramid B: use ratio of 25:1 and multiply 16 by 25 to find 400, and root 5 to 125
If cos 0 = 3/radical 22 and angle 0 is in Quadrant I, what is the exact value of tan 20 in
simplest radical form?
Answer:
[tex] \tan2\theta =-\dfrac{3\sqrt{13}}{2} [/tex]Step-by-step explanation:
To find:-
The value of [tex]\tan2\theta[/tex] .Answer:-
We are here given that the value of,
[tex]\longrightarrow \cos\theta=\dfrac{3}{\sqrt{22}} \\[/tex]
And we know that cosine is the ratio of base and hypotenuse. Therefore,
[tex]\longrightarrow \cos\theta =\dfrac{b}{h} \\[/tex]
So we can also say that,
[tex]\longrightarrow \cos\theta = \dfrac{b}{h}=\dfrac{3}{\sqrt{22}}\\[/tex]
Let us take the given ratio to be 3x:√22x . Now we may find out the value of perpendicular using Pythagoras theorem . The Pythagoras theorem is ,
Pythagoras theorem:-
In a right angled triangle the sum of squares of perpendicular and base is equal to the square of hypotenuse.Mathematically,
[tex]\longrightarrow \boxed{ \boldsymbol{p^2+b^2=h^2}} \\[/tex]
where the symbols have their usual meaning.
On substituting the respective values, we have;
[tex]\longrightarrow p^2+(3x)^2=(\sqrt{22}x)^2 \\[/tex]
[tex]\longrightarrow p^2 = 22x^2-9x^2\\[/tex]
[tex]\longrightarrow p^2=13x^2 \\[/tex]
[tex]\longrightarrow \boldsymbol{ p = \sqrt{13}x} \\[/tex]
Now again , we know that, tangent is defined as the ratio of perpendicular and base. Therefore,
[tex]\longrightarrow \tan\theta = \dfrac{p}{b} \\[/tex]
[tex]\longrightarrow \tan\theta = \dfrac{\sqrt{13}x}{3x}\\[/tex]
[tex]\longrightarrow \boldsymbol{ \tan\theta = \dfrac{\sqrt{13}}{3}}\\[/tex]
Now we may use a identity which is ,
[tex]\longrightarrow\boxed{ \boldsymbol{ \tan (2x)= \dfrac{2\tan x}{1-\tan^2 x}}}\\[/tex]
On substituting the respective values, we have;
[tex]\longrightarrow \tan2\theta = \dfrac{ 2\tan\theta}{1- \tan^2\theta}\\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{2\bigg(\dfrac{\sqrt{13}}{3}\bigg)}{1-\bigg(\dfrac{\sqrt{13}}{3}\bigg)^2 } \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{1-\dfrac{13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{9-13}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{-4}{9}} \\[/tex]
[tex]\longrightarrow \tan2\theta = -\dfrac{2\sqrt{13}\cdot 9}{3\cdot 4 } \\[/tex]
[tex]\longrightarrow \boxed{\boldsymbol{ \tan2\theta = -\dfrac{3\sqrt{13}}{2}}} \\[/tex]
This is the required answer .
Given the arithmetic sequence of 21,
6, 9, 24,
find an explicit rule for the nth term.
Answer:
Step-by-step explanation:
The sequence you gave is not arithmetic. I'm assuming the sequence is
21, 6, -9, -24.
d is the common difference between adjacent terms.
a₂ = a₁ + d
6 = 21 + d
d = -15
nth term = a₁ + (n-1)d = 21 - (n-1)15
A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg. The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches. The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?
A. The system has two solutions, but only one is viable because the other results in negative side lengths.
B. The system has only one solution, and it is viable because it results in positive side lengths.
C. The system has only one solution, but it is not viable because it results in negative side lengths
. D. The system has two solutions, and both are viable because they result in positive side lengths.
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
Took the plato test and passed it, I don't know what the purpose of the first answer is, but here is the correct answer.
1355 + 0540 add as n military time btw this is a military time answer also im on mobymax
Answer:
1895
Step-by-step explanation:
A researcher for a travel company is looking into the prices people are willing to pay for airplane tickets. The company has communicated that the overall population mean is $265 with a standard deviation of $40.93. The researcher has a sample of 130 ticket purchases from one location. By the central limit theorem, which interval can the researcher be 95% certain that the sample mean will fall within?
A.
$261.41 and $268.59
B.
$257.82 and $272.18
C.
$264.37 and $265.63
D.
$254.23 and $275.77
Answer:
I believe answer B.
Watch help video
Given 1 ||
т
||
n, find the value of x.
Z
(4x+6)°
т
(5x-4)
n
Hi please help me with these questions asap.
Step-by-step explanation:
A. r=42/2=21
B.
[tex] {21}^{2} \pi + 60 \times 42 = \\ = 441\pi + 2520[/tex]
C.
[tex]42\pi + 60 \times 2 = \\ = 42\pi + 120[/tex]
someone help me please
Step-by-step explanation:
Hi,
You will have to move the pre-image 15 units to the right. You're also going to have to flip the image horizontally (kind of like flipping it across the x-axis) and after that, you're going to have to flip it so that it's facing the left side.
1) 15 units right
2) Flip-up
3) Flip to the left
Hope this helps :)
The mean annual starting salaries for college graduates with a degree in Operations Management was $65,000. We would like to determine whether or not this has decreased this year due to the pandemic. Data were collected over the annual starting salaries from a random sample of 40 Operations Management graduates. The average salary is $63,500 in the sample. Assume the standard deviation for the population of annual salaries is $3500. Let denote the average annual starting salaries among all Operations Management graduates this year.
Required:
What is the value of the appropriate test statistic?
Answer:
The value of the appropriate test statistic is Z = -2.71.
Step-by-step explanation:
The mean annual starting salaries for college graduates with a degree in Operations Management was $65,000. We would like to determine whether or not this has decreased this year due to the pandemic.
This means that the null hypothesis is that the mean stays the same, that is:
[tex]H_0: \mu = 65000[/tex]
The alternative hypothesis is that it decreased, that is:
[tex]H_a: \mu < 65000[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
65000 is tested at the null hypothesis:
This means that [tex]\mu = 65000[/tex]
Data were collected over the annual starting salaries from a random sample of 40 Operations Management graduates. The average salary is $63,500 in the sample. Assume the standard deviation for the population of annual salaries is $3500.
This means that [tex]n = 40, X = 63500, \sigma = 3500[/tex]
What is the value of the appropriate test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{63500 - 65000}{\frac{3500}{\sqrt{40}}}[/tex]
[tex]Z = -2.71[/tex]
The value of the appropriate test statistic is Z = -2.71.
Need answer asap, correct answer will get brainliest.
Answer: D
Step-by-step explanation: To reflect each point across the y-axis you take the opposite of the x-coordinate
Can someone please give me the answer I will mark u brilliant
Answer:
200
Step-by-step explanation:
Volume of juice
[tex] = 3.5 \times 6 \times 9 \\ = 189 \\ \approx \: 200 \: {cm}^{3} [/tex]
30 points for this A special truck cleans the surface of the ice rink shown. The figure is composed of a square and two semicircles.
85 ft
85 Ft
If the truck cleans the entire surface, how many square feet of ice will the truck clean?
Use 3.14 for . Round your answer to the nearest tenth.
The truck will clean about
square feet of ice
Answer:
12897 square feet
Step-by-step explanation:
So first find the area of the square:
85 * 85 = 7225
Then, the two semi circles together is a full circle. Use the circle area formula,
A = πr^2
The radius (r) would be half the diameter of the circle. The diameter of the circle would be 85. So half of that is 42.5. The radius is 42.5
Now:
A = π(42.5)^2
A = 3.14(42.5)^2
A = 3.14(1806.25)
A = 5671.625
Lastly, add the two areas up for the square and circle:
7225 + 5671.625 = 12896.625
Round to nearest tenth: 12897
Find TWO factors that are equivalent to 1/2
Answer:
6/12, 4/8
Step-by-step explanation:
What does p equal Help?
Answer:
your answer will be P=27
Step-by-step explanation:
hope it helps...
If n and k are positive integers and 8” = 2*, what is the value of n/k
Answer:
B) 1/3
Step-by-step explanation:
If n=1 and k=3, then 8^n=2^k is true. Therefore, n/k=1/3.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 8 N acts on a certain object, the accelerstion of the object is 4 m/s2. If the acceleration of the object becomes 9 m/s?, what is the force?
Answer:
18N
Step-by-step explanation:
According to Newtons second law
F ∝ a
F = ka
k is the constant of proportionality
When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s2, hence;
8 = 4k
k = 8/4
k = 2
If a = 9m/s², F = ?
Recall F = ka
F = 2 * 9
F = 18N
Hence the force will be 18N
Can someone help me solve for x please it’s urgent
Answer:
37.5
Step-by-step explanation:
16/46 = 20/(20+x)
or, 16(20+x) = 46×20
or, 320 + 16x = 920
or, 16x = 600
or, x = 600/16
x = 37.5
Need help on this please still lost on this one
How much time will it take for a bug to travel 75 meters across the floor if it is traveling at 5 m/s?
What is the surface area? 4 mm 10 mm 5mm square millimeters
Answer:
200
Step-by-step explanation:
Length*Width*Hight= 4*10*5=200
hope this helps
Answer: I am pretty sure it is 200
Step-by-step explanation:
I may be wrong sorry if it is have a good day :)
Express the shaded area as a fraction, a decimal, and a percent of the whole
Answer:
Fraction : 3/9
Decimal : 0.33333333 (the .3 continues)
Percent : 33.33333%
Step-by-step explanation:
Dividing 3 by 9 will give you a continous set of 3.
The distance around a circle is 69.08 feet. Determine the area of the circle.
Answer:
138.16
Step-by-step explanation:
Which value of b would make 16x? - bx + 25 a perfect square trinomial?
a. 4
b. 5
C. 20
d. 40
9514 1404 393
Answer:
d. 40
Step-by-step explanation:
Consider the square ...
(px +q)² = (px)² +2(px)(q) +q² = p²x² +2pqx +q²
Comparing this to your expression, you see ...
16 = p² ⇒ p = ±4
25 = q² ⇒ q = ±5
-b = 2pq = 2(±4)(±5) = ±40
The expression is a perfect square trinomial when b = 40.
_____
Additional comment
When the linear term has a negative coefficient, we know the signs of the binomial terms are different. We conventionally write the square with the constant term in the binomial being negative:
16x² -40x +25 = (4x -5)²
Please help me in this
Answer:
top=170mm squared
shape 2=76.27 cm squared
shape 3=62.862 cm squared
Step-by-step explanation:
top shape...
(18x15)-4(5x5)=area
270-4(25)=area
270-100=area
170=area
shape 2...
diameter of circle is 6 so radius is 3...
area=pier^2
a=28.27 and their are two half circles so that makes one whole circle
(8x6)+28.27=76.27 cm squared
shape 3...
total of rectangle with a half circle subtracted. r=4 d=8
so
11x8=88 for rectangle then subtract half circle
a=pie r^2
a=50.27
50.27/2=25.135 subtract this from rectangle total...
88-25.135=62.862 cm squared
please help me i really need help please i really really need help please
Answer:
56.6 yd
Step-by-step explanation:
in the picture above
pls mark as brainliest
Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
OA 3
OB.
5
OC. 6
OD 10
PL HELP WILL MARK BRAINLY 10 POINTS
Answer:
5 times
Step-by-step explanation:
1/6·30=5
so your answer is b)5
Can i have a brainliest please or 10 points?